Demand-side management is increasingly important for low-carbon transport governance. However, many studies assume relatively stable travel preferences and pay limited attention to behavioural changes under sudden external shocks. This study proposes an Event–Behaviour–Resilience framework and applies Natural Language Processing to Sina Weibo data to examine travel responses to extreme heat and refined oil price adjustments. The results show asymmetric response patterns. Oil price increases were associated with cost-based low-carbon substitution, with new-energy vehicle intentions accounting for 64.4% of the share. In contrast, extreme heat was associated with both trip reduction and motorised travel. Travel reduction reached 52.4%, while ride-hailing or taxi responses accounted for 24.6%. A quadratic fitting analysis identified 38.0–39.0 °C as an observed transition interval, within which high-carbon motorised willingness began to exceed low-carbon slow mobility willingness. Group-level analysis showed unequal behavioural flexibility. While 80.0% of the general population reduced travel under extreme heat, the forced mobility group showed limited travel reduction and maintained a high level of low-carbon willingness at 86.87%. XGBoost-SHAP results indicated that temperature, emotional valence, and behavioural constraints contributed to low-carbon mobility intention. These findings suggest that behavioural responses can help identify spatial interventions for low-carbon transport, especially in relation to heat exposure, mobility flexibility, and access to adaptive travel options.